Title: Ricci flow from spaces with isolated conical singularities
Felix Schulze (University College London)
Abstract: Let (M,g_0) be a compact n-dimensional Riemannian manifold with a
finite number of singular points, where at each singular point the metric is asymptotic
to a cone over a compact (n-1)-dimensional manifold with curvature operator greater
or equal to one. We show that there exists a smooth Ricci flow, possibly with isolated
orbifold points, starting from such a metric with curvature decaying like C/t.
The initial metric is attained in Gromov-Hausdorff distance and smoothly away from
the singular points. To construct this solution, we desingularize the initial metric by
glueing in expanding solitons with positive curvature operator, each asymptotic to the
cone at the singular point, at a small scale s. Localizing a recent stability result of
Deruelle-Lamm for such expanding solutions, we show that there exists a solution
from the desingularized initial metric for a uniform time T>0, independent of the
glueing scale s. The solution is then obtained by letting s->0. We also show that the
so obtained limiting solution has the corresponding expanding soliton as a forward
tangent flow.